The present invention relates to power systems, and more particularly, to methods and apparatus for differential current measurement in three-phase power systems.
Differential current measurement is a technique used in a wide variety of power system applications. For example, the technique is often used in the protection of power system equipment, such as transformers, generators, motors, and the like. Generally, differential current measurement techniques involve monitoring the current at both an input terminal and an output terminal of a device, normalizing the measured input and output currents to compensate for changes in phase and magnitude of the measured currents that may be introduced by the device during normal operation, and then comparing the normalized input and output currents. If the difference between the normalized input and output currents is zero, then the device presumably is working properly. On the contrary, a detected difference between the normalized input and output currents may indicate a fault within the device. In response to the detection of a fault, a relay or other circuit breaker may be triggered to shut off power to the device in order to prevent further damage.
FIG. 1 is an example of how differential current measurement may be employed in the protection of a three-phase power distribution transformer 10. As shown, each phase a, b, and c of the power system is connected to a respective primary winding (high-voltage side) of the transformer 10 via a respective input of a first terminal 12. Similarly, a second terminal 14 provides an output from the secondary winding for each phase (low-voltage side). Current transformers 16a, 16b, and 16c can be used to obtain a measure of the current flowing into each phase of the first terminal (I1a, I1b, and I1c). Similarly, a measure of the current flowing out of each phase of the second terminal (I2a, I2b, and I2c) can be obtained by respective current transformers 18a, 18b, and 18c. 
Transformers like that shown in FIG. 1 are often employed either to step-up or step-down an input voltage or current. This naturally introduces a change in the magnitude of the voltage or currents entering and leaving the device. With a transformer, the magnitude of this change is dependent upon the ratio of the number of turns, N1, in the primary winding of the transformer to the number of turns, N2, in the secondary winding. Specifically, the input current (I1) to the primary winding will be equal to N2/N1 times the current output from the secondary winding (I2). Thus, I1=N2/N1(I2). The turns ratio of the transformer must be taken into account when normalizing the input and output currents during the differential current measurement process.
The magnitude and phase of the input currents can also be affected during normal operation of a transformer by the manner in which the primary windings (high-voltage side) for each phase and the secondary windings (low-voltage side) for each phase are connected, or wired. Two common ways to wire the multi-phase windings on one side of a transformer are referred to in the art as the Wye (Y) configuration and the Delta (xcex94) configuration. Different combinations of these and other configurations can be used to wire the respective primary and secondary windings. In the example of FIG. 1, the primary windings of the transformer are connected in a Wye (Y) configuration, and the secondary windings are connected in a delta (xcex94) configuration. A Y-xcex94 wiring configuration of this type will introduce a phase shift of 30 degrees, and a change in magnitude between the input and output currents by a factor of 1/{square root over (3)}. That is, ignoring the turns ratio, I1=1/{square root over (3)}∠+30xc2x0 (I2), where I1 is the input current to the primary winding and I2 is the output current from the secondary winding. Other wiring configurations will result in other phase shift magnitudes. Generally, the known wiring configurations for distribution transformers in use in the power distribution industry induce phase shifts that are some multiple of 30xc2x0. Different phase shifts result in different changes in current magnitude. These changes in magnitude and phase must also be taken into account when normalizing the input and output currents during the differential current measurement process.
With respect to the phase and magnitude changes caused by the wiring configuration at the primary and secondary windings, one way to cancel out those changes to achieve normalization is to wire the current transformers 16a-c, 18a-c in such a way as to cancel out the affect of the transformer wiring configuration. Generally, however, power distribution system customers do not favor such a solution, particularly because the variety of different wiring configurations for the primary and secondary transformer windings requires a different current transformer wiring configuration to provide the appropriate normalization in each case. Consequently, this form of physical normalization, commonly referred to as current transformer phasing, makes transformer installation much more difficult and costly.
Because of the difficulties with current transformer phasing, the general approach to normalization with respect to magnitude and phase changes caused by the wiring configurations of transformers today is to digitize the measured currents obtained with the current transformers 16a-c, 18a-c, and to then perform the normalization functions digitally on a programmable processor or microcontroller. In this manner, different transformer wiring configurations can be accommodated by simply reprogramming the processor for each different case, while using the same physical connection for the current transformers. Transformer installation is thus simplified and less costly.
FIG. 1 illustrates this form of digital processing. As shown, the current measurements obtained by the respective sets of input and output current transformers 16a-c, 18a-c, are digitized and passed through respective normalization functions 20, 22 to produce normalized input ({overscore (I1a)}, {overscore (I1b)}, and {overscore (I1c)}) and output ({overscore (I2a)}, {overscore (I2b)}, and {overscore (I2c)}) currents in which changes in magnitude and phase introduced by the transformer 10 during normal operation are factored out. A differential current function 24 then calculates a differential current for each phase from the normalized input and output currents (IOpa={overscore (I1a)}xe2x88x92{overscore (I2a)}; IOPb={overscore (I1b)}xe2x88x92{overscore (I2b)}; and IOPc={overscore (1c)}xe2x88x92{overscore (I2c)}). During normal operation of the transformer 10, each IOP current should equal zero. However, a fault within the transformer 10 should result in a non-zero reading. The non-zero reading can be used as an indication of a transformer fault. Upon detecting such a non-zero reading, a relay or circuit breaker can be triggered to interrupt power to the transformer to prevent further damage.
Another consideration to be taken into account in performing differential current measurements in a multi-phase power system, particularly in differential current measurements used for protection of transformers, is the presence of a zero-sequence current component. Power system connections that allow ground or zero sequence current to flow will add to the individual phase currents, and where it is present on only one side of the device will create a non-zero combination that will result in a false differential current reading that could be interpreted as a fault within the device (i.e., xe2x80x9cinternal faultxe2x80x9d) when in actuality the fault has occurred in the line outside of the device (i.e., xe2x80x9cexternal faultxe2x80x9d or xe2x80x9cthrough faultxe2x80x9d). Because of this possibility, in addition to compensating for the phase shifts introduced by the device, it is also necessary for the normalization technique to eliminate the zero-sequence current component when calculating the appropriate normalization factor.
For three-phase power systems, the normalization calculations, including the removal of the zero-sequence current component, can be reduced to a 3xc3x973 matrix transform. Indeed, the power transformer industry has developed a series of such matrix transforms to perform normalization and zero-sequence current component removal for the different multiples of 30xc2x0 phase shifts that result from the various wiring configurations commonly in use in the industry. For example, the normalization required on the currents measured from the secondary winding (low-voltage side) of the transformer 10 in the example of FIG. 1 (where the phase shift is 30xc2x0), with the removal of the zero-sequence component, can be achieved with the following matrix transform calculation:       [          xe2x80x83        ⁢                                                      I                              2                ⁢                a                                      _                                                                          I                              2                ⁢                b                                      _                                                                          I                              2                ⁢                c                                      _                                ⁢          xe2x80x83        ]    =                    1                  3                    [              xe2x80x83            ⁢                                    1                                              -              1                                            0                                                0                                1                                              -              1                                                                          -              1                                            0                                1                              ⁢              xe2x80x83            ]        ⁢          xe2x80x83        [                                        I                          2              ⁢              a                                                                        I                          2              ⁢              b                                                                        I                          2              ⁢              c                                            ⁢          xe2x80x83        ]  
where {overscore (I2a)}, {overscore (I2b)}, and {overscore (I2c)} are the normalized current values (ignoring the turns ratio) for the measured currents I2a, I2b, and I2c obtained from the current transformers 18a, 18b, and 18c, respectively. Similarly, elimination of the zero-sequence component from the current measurements obtained on the high-voltage side can be obtained using the following matrix transform for a 0xc2x0 phase reference:       [          xe2x80x83        ⁢                                                      I                              1                ⁢                a                                      _                                                                          I                              1                ⁢                b                                      _                                                                          I                              1                ⁢                c                                      _                                ⁢          xe2x80x83        ]    =                    1        3            ⁢              xe2x80x83            [              xe2x80x83            ⁢                                    2                                              -              1                                                          -              1                                                                          -              1                                            2                                              -              1                                                                          -              1                                                          -              1                                            2                              ⁢              xe2x80x83            ]        ⁢          xe2x80x83        [                                        I                          1              ⁢              a                                                                        I                          1              ⁢              b                                                                        I                          1              ⁢              c                                            ⁢          xe2x80x83        ]  
where {overscore (I1a)}, {overscore (I1b)}, and {overscore (I1c)} are the normalized current values (ignoring the turns ratio) for the measured currents I1a, I1b, and I1c obtained from the current transformers 18a, 18b, and 18c, respectively.
FIG. 1A is a table providing the standard matrix transforms for the different multiples of 30xc2x0 phase shifts that the various industry standard transformer wiring configurations may introduce. During set-up of a transformer protection device that performs differential current measurements using such matrix calculations, the technician will select the appropriate transforms (high-voltage side and low-voltage side) from the table of FIG. 1A and program the protection device to perform normalization of the measured input and output currents in accordance with the selected transforms. Typically, the 0xc2x0 transform will be used as the reference transform on the high-voltage side of the transformer, as in the example above.
While the use of digital processing and the standard matrix transforms listed in the table of FIG. 1 A has simplified the installation of power system equipment that relies upon differential current measurement techniques, there are still disadvantages and drawbacks to the use of these matrix transforms. First, a technician is still required to select the appropriate transforms from the table based on the physical connections of the equipment and to then program the equipment to perform those transforms. Second, while these transforms work for ideal phase shifts that are multiples of 30xc2x0, they cannot compensate for non-ideal device physics that might cause slight variations in the expected theoretical phase shift. Third, these transforms obviously do not enable a device to perform dynamic phase shift compensation; rather, a single transform is selected by a technician based on the device connections and that transform is then used exclusively. Because of these drawbacks, there is a need for a differential current measurement technique that performs the appropriate normalization, including removal of the zero-sequence component, for any phase shift (thus being capable of handling non-ideal device physics), and that can perform such normalization dynamically. The present invention satisfies this need.
The present invention is directed to a method and apparatus for measuring the differential current between a first terminal and a second terminal of a device in a three-phase power system, where the device introduces a difference in phase between the current through the first terminal and the current through the second terminal. The method and apparatus of the present invention can be used in a wide variety of power system applications in which differential current measurements are needed, such as, for example, in the protection of power system equipment, such as transformers, generators, motors, and the like. According to the present invention, a measure of the current through the first terminal is obtained for each phase of the three-phase power system, and a measure of the current through the second terminal is obtained for each phase. The measured currents obtained for each phase at the first and second terminals are then normalized to compensate for any changes in phase introduced by the device. The normalization is performed using a novel, generalized transform having the form:
G(xcex8)=cos(xcex8)U+sin(xcex8)J
where U represents a unit zero degree phase shift with zero sequence components removed, and J represents a unit ninety degree phase shift with zero sequence components removed. The normalized currents are then used to calculate a differential current measurement for each phase.
The generalized transform G(xcex8) properly normalizes the measured currents for any phase angle difference between them; that is, the generalized transform G(xcex8) works for all xcex8 from 0 to 2xcfx80. Moreover, because the generalized transform works for any phase shift, it provides correct normalization even in the presence of non-ideal device physics. Furthermore, because the generalized transform works for any phase shift, the generalized transform can be used in conjunction with a phase measurement device to provide dynamic normalization as the phase shift between the input and output currents of a device varies over time.
Other features and advantages of the present invention will become evident hereinafter.